Inverse Kinematics Solutions for Serial Robots using Support Vector Regression Antonio Morell, Mahmoud Tarokh † and Leopoldo Acosta (Member, IEEE ) Department of Systems Engineering and Control and Computer Architecture University of La Laguna, 38203 La Laguna, Tenerife, Spain email: amorell@isaatc.ull.es, lacosta@ull.es † Department of Computer Science, San Diego State University, San Diego, CA 92182–7720, U.S.A. email: tarokh@cs.sdsu.edu Abstract—Serial kinematic chains are widely used in robotics and computer animation among other fields. Many manipulators do not have closed–form solutions to the inverse kinematics problem, which is of great importance for many applications. In this paper we introduce a fast and accurate procedure which yields all joint angle solutions for a given manipulator or limb posture (position and orientation) and certain swivel angle. By means of a spatial decomposition method, the procedure involves finding accurate models which represent the behavior of the robot or limb in a given workspace region. We propose Support Vector Machines, a very popular machine learning method, as the method that models such behaviors. The performance of the method is tested on the Robotic Research Arm K–1207. The results confirm that the method finds accurate solutions and can be used on real world applications with real–time requirements. I. I NTRODUCTION We define a configuration of a manipulator as a set of joints angle, and a posture as the position and orientation of its end effector (hand or foot in a human–like figure). The Inverse Kinematics Problem (IKP) is stated as the process of finding the set of all configurations that result in a given posture in the workspace. Many articulated manipulators with joint offsets do not have closed–form solutions, and the computation of their inverse kinematics is complex and time consuming and therefore unsuitable for real–time applications. Whereas some classes of serial manipulators actually have an algebraic inverse kinematics solution, the analytical expressions have to be defined for each specific morphology [1]. During last decades, several methods for solving the IKP have been proposed, such as Jacobian based methods (pseu- doinverse, transpose and damped least squares) [2], genetic algorithms [3], continuation [4] and interval [5] methods. However, some of them do not guarantee all the possible solutions for a given manipulator pose. In addition, they might have convergence problems and high computational require- ments, which usually makes them unsuitable for real–time ap- plications. The spatial decomposition method has proven to be suitable for solving kinematics [6] and planning problems [7] which usually have non trivial and complex solutions, if any. It provides simple steps to obtain a model of the behavior of a given robot or limb through its workspace, in order to determine accurate solutions for the inverse kinematics problem for serial manipulators, and similarly, the forward kinematics problem for parallel robots [8]. The most important feature of this method is its ability to yield accurate solutions with a small evaluation time, which enables it to be used in real–time applications. In this context, this paper presents a spatial decomposition method for obtaining accurate solutions in real–time for the IKP for serial manipulators and kinematic chains, using a popular machine learning method, the Support Vector Ma- chines (SVMs), as the regression model. Using SVMs as the modeling tool allows to obtain accurate approximations of the solutions as well as small evaluation times, while the overall complexity of the method decreases. The yielded results are compared with the polynomial method proposed by [6] using the same case study. This paper is organized as follows. Section II discusses the inverse kinematics problem for serial robots and kinematic chains. Section III describes the first steps of the method, where the workspace of a robot is decomposed into small cells, which are populated with a large amount of configuration and posture data point. Then, these datapoints are classified as described in Section IV, in order to obtain meaningful training data sets for the modeling step with SVMs, that is introduced in Section V. Finally, the evaluation step, which is done on–line, is illustrated in Section VI. Some experiments have been performed and are shown in Section VII, where we compare our results with those obtained by the very fast approximation method proposed in [6]. II. IKP ON SERIAL ROBOTS AND KINEMATIC CHAINS Serial kinematic chains are present in a wide variety of fields and applications in robotics and computer animation. They are often implemented as 7 Degrees of Freedom (DOF) kinematic chains, modeled similarly to the human arm (or leg), with a 3–DOF spherical joint as a shoulder (hip), another 3–DOF for the wrist (ankle), and a single DOF revolute joint for the elbow (knee) [9]. An example of a typical 7–DOF serial robot is the Robotic Research Arm K–1207 manipulator [10]. The model which represents the configurations and postures for this robot can be described by the Denavit–Hartenberg (D–H) 2013 IEEE International Conference on Robotics and Automation (ICRA) Karlsruhe, Germany, May 6-10, 2013 978-1-4673-5642-8/13/$31.00 ©2013 IEEE 4188